Hyperbola Tangent Intercepts and Midpoint Locus

Hyperbola Tangent Intercepts and Midpoint Locus
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2017-04-01 17:53
This example demonstrates the locus of the midpoint of the line segment connecting the x and y intercepts of tangents drawn from a point on a hyperbola. It involves core concepts like hyperbolas, tangent lines, coordinate geometry, midpoint formulas, and locus equations. Constructed using GeoGebra commands such as CurveCartesian, Point, Tangent, Intersect, and Midpoint. Suitable for high school and above students studying hyperbola properties, tangent applications, and locus problems.

GeoGebra Commands & Parameters

  1. CurveCartesian(((a * sec(t)), (b * tan(t))), t, 0, (2 * 3.141592653589793)) → c
  2. Point(c) → A
  3. Tangent(A, c) → f
  4. Intersect(f, xAxis) → B
  5. Intersect(yAxis, f) → C
  6. Midpoint(B, C) → D